Problem 1. Drones [6 points]

A risk-neutral consumer is in the market for a drone to fly around town taking video. The consumer's value for the drone is $1000 if it is operative, and $0 if it fails. Producer A makes drones with a 5% chance of failure.

(a) (1 points). What is the consumer's willingness to pay for the drone? It costs Producer A $800 to make the drone, and they price it exactly at the consumer's willingness to pay that you found above. Everything is hunky dory until a knockoff drone supplier, Producer B, realizes they can enter the market and make money by selling an inferior product that costs $400 to make, but that has a 50% failure rate, which is indistinguishable to the consumer from the more reliable drone.

(b) (2 points). If this new entrant were to provide as many drones as the other supplier (i.e. Producer A produces 50% of the market and Producer B produces 50% of the market so that the chance of getting a drone from either company is 50%), what is the consumer's willingness to pay for a random drone they purchase?

(c) (1 points). Suppose in the short-run, the price is set exactly equal to what you found in part b. What is the short-term profit per drone of Producer B?

(d) (2 points). Given what you found in (c) and (d), what will be the equilibrium price for drones, and the market share of the two companies?

(e) (1 points). Producer A can hire an independent testing agency to show that their drones are indeed better than those from Producer B, and only have a 5% failure rate. The consumers will believe the certification of this tester. Assuming there are 1 million potential customers for drones each year, and Producer A would get back 50% of the market with the new certification, how much is Producer A willing to pay for this service annually?